Reeb graphs are structural descriptors that capture shape properties of a topological space from the perspective of a chosen function. In this work we define a combinatorial metric for Reeb graphs of orientable surfaces in terms of the cost necessary to transform one graph into another by edit operations. The main contributions of this paper are the stability property and the optimality of this...

In order to develop statistical methods for shapes with a tree-structure, we construct a shape space framework for treeshapes and study metrics on the shape space. This shape space has singularities, which correspond to topological transitions in the represented trees. We study two closely related metrics on the shape space, TED and QED. QED is a quotient Euclidean distance arising naturally fr...

We model the edit distance as a function in a labelling space. A labelling space is an Euclidean space where coordinates are the edit costs. Through this model, we define a class of cost. A class of cost is a region in the labelling space that all the edit costs have the same optimal labelling. Moreover, we characterise the distance value through the labelling space. This new point of view of t...

In the last few years, computing environments for human learning have rapidly evolved due to the development of information and communication technologies. However, the use of information technology in automatic correction of spelling errors has become increasingly essential. In this context, we have developed a system for correcting spelling errors in the Arabic language based on language mode...

Card sorts are a knowledge elicitation technique in which participants are given a collection of items and are asked to partition them into groups based on their own criteria. Information about the participant’s knowledge structure is inferred from the groups formed and the names used to describe the groups through various methods ranging from simple quantitative statistical measures (e.g. co-o...

We investigate some operations where essentially, from a given word w, the word ww′ is constructed where w′ is a modified copy of w or a modified mirror image of w. We study whether ww′ is a primitive word provided that w is primitive. For instance, we determine all cases with an edit distance of w and w′ at most 2 such that the primitivity of w implies the primitivity of ww′. The operations ar...

Most research on the edit distance problem and the k-differences problem considered the set of edit operations consisting of changes, insertions, and deletions. In this paper we include the swap operation that interchanges two adjacent characters into the set of allowable edit operations, and we present an O(t min(m, n))-time algorithm for the extended edit distance problem, where t is the edit...

The string correction problem looks at minimal ways to modify one string into another using fixed operations, such as for example inserting a symbol, deleting a symbol and interchanging the positions of two symbols (a “swap”). This has been generalized to trees in various ways, but unfortunately having operations to insert/delete nodes in the tree and operations that move subtrees, such as a “s...

Edit Distance has been widely studied and successfully applied in a large variety of application domains and many techniques based on this concept have been proposed in the literature. These techniques share the property that, in case of patterns having different lengths, a number of symbols are introduced in the shortest one, or deleted from the longest one, until both patterns have the same l...

A common model for computing the similarity of two strings X and Y of lengths m, and n respectively with m n, is to transform X into Y through a sequence of edit operations which are of three types: insertion, deletion, and substitution of symbols. The model assumes a given weight function which assigns a non-negative real cost to each of these edit operations. The amortized weight for a given ...